Question

The average age of 10 children is 14 years. If two children of ages 13 years and 10 years left this group and another two children having ages 7 years and 6 years joined, then the average age of this new group is x. If the two children who left from the original group rejoins this new group, then the average age of this group is less than x by:

• A. 3/4
• B. 1/4
• C. 7/4
• D. 15/14

Hint:

Average = $\frac{\text{Total Sum}}{\text{Number of observations}}$.

Answer 1

The Correct Option is B

Step 1: Concept
Averages and sum of observations.

Step 2: Analysis
Initial sum = $10 \times 14 = 140$.
Sum after 2 left and 2 joined = $140 - (13 + 10) + (7 + 6) = 140 - 23 + 13 = 130$.
New average $x = \frac{130}{10} = 13$.

Step 3: Calculation
Sum when the original two rejoin = $130 + 23 = 153$.
Total children = $10 + 2 = 12$.
New average = $\frac{153}{12} = 12.75$.
Difference = $13 - 12.75 = 0.25 = 1/4$.

Step 4: Conclusion
Hence, the average is less than x by 1/4. Final Answer: (B)